Mathematical Complexity of Computational Modeling Experiences for - - PowerPoint PPT Presentation

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Mathematical Complexity of Computational Modeling Experiences for - - PowerPoint PPT Presentation

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Mathematical Complexity of Computational Modeling Experiences for Elementary Students Kevin W. McElhaney, Gautam Biswas, Jennifer L. Chiu STEM+C PI Summit Challenges Showcase September 19, 2019 Curricular context: Modeling urban water runoff

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Kevin W. McElhaney, Gautam Biswas, Jennifer L. Chiu STEM+C PI Summit Challenges Showcase September 19, 2019

Mathematical Complexity of Computational Modeling Experiences for Elementary Students

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Curricular context: Modeling urban water runoff

  • Multi-week, 5th grade curriculum unit integrating

earth science, engineering, and computational thinking (NGSS PEs 5-ESS3-1, 3-5ETS1-3)

  • Students develop a computational model of water

runoff and use it to test and refine engineering solutions

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Designing the runoff model

Runoff model

Science DCIs (Human impacts/ Runoff) SEPs (e.g., modeling, information, investigation) CCCs (e.g., Systems and system models, matter) Engineering DCIs (e.g., develop, test, refine solutions) CT concepts & practices (e.g., creating and testing computational artifacts, loops, variables…)

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Basic runoff system model

s u r f a c e rainfall absorption (material dependent) runoff (rainfall – absorption)

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Runoff algorithm (time dependent)

set StormDuration to... set ElapsedTime to 0 set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

variable initialization simulation with stopping condition

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Runoff algorithm (time dependent)

set StormDuration to... set ElapsedTime to 0 set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Temporal variables require reasoning about rates and durations

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Runoff algorithm (time dependent)

set StormDuration to... set ElapsedTime to 0 set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Hourly vs. total variables

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Runoff algorithm (time dependent)

set StormDuration to... set ElapsedTime to 0 set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

“set” vs. “change”

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Runoff algorithm (time dependent)

set StormDuration to... set ElapsedTime to 0 set HourlyRainfall to... set TotalAbsorption to 0 set TotalRunoff to 0 set TotalRainfall to 0 set AbsorptionCoeff to... Repeat until (ElapsedTime is equal to StormDuration) change ElapsedTime by 1 change TotalRainfall by HourlyRainfall change TotalAbsorption by ... set TotalRunoff to TotalRainfall – TotalAbsorption

Repeat until (stopping condition) is challenging

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Runoff algorithm (not time dependent)

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Runoff algorithm (not time dependent)

set TotalRainfall to... set AbsorptionLimit to... if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

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Runoff algorithm (not time dependent)

set TotalRainfall to... set AbsorptionLimit to... if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

No rate-based or temporal variables

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Runoff algorithm (not time dependent)

set TotalRainfall to... set AbsorptionLimit to... if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

No “change”

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Runoff algorithm (not time dependent)

set TotalRainfall to... set AbsorptionLimit to... if (TotalRainfall is equal to AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is less than AbsorptionLimit) set TotalAbsorption to TotalRainfall set TotalRunoff to 0 if (TotalRainfall is greater than AbsorptionLimit) set TotalAbsorption to AbsorptionLimit set TotalRunoff to TotalRainfall – TotalAbsorption

Simpler conditions; no nesting

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Designing the runoff model

Runoff model Science DCIs (Human impacts/ Runoff) SEPs (e.g., modeling, information, investigation) CCCs (e.g., Systems and system models, matter) Engineering DCIs (e.g., develop, test, refine solutions) CT concepts & practices (e.g., programming, algorithms, variables…)

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Designing the runoff model

Runoff model Science DCIs (Human impacts/ Runoff) SEPs (e.g., modeling, information, investigation) CCCs (e.g., Systems and system models, matter) Engineering DCIs (e.g., develop, test, refine solutions) CT concepts & practices (e.g., programming, algorithms, variables…)

Grade-appropriate mathematics concepts

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Summary

  • Computational modeling experiences are

constrained by grade-appropriate mathematics concepts, especially in elementary

  • Designers may be challenged to align multiple

educational frameworks (NGSS, CS Framework, CCSSM) at specific grade levels

  • Argues for a broad definition of “computational

model” for STEM+C education

  • model that leverages computational affordances (e.g.,

facilitates rapid testing and iterative refinement)

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Project team

SR SRI

  • Nonye Alozie
  • Satabdi Basu
  • Ron Fried
  • Reina Fujii
  • HeeJoon Kim
  • Jennifer Knudsen
  • Beth McBride

UV UVA

  • Chris Dittrick
  • Sarah Fick
  • James Hong
  • Sarah Lilly
  • Anne McAlister

Vanderbilt ilt

  • Ningyu Zhang

Acknowledgements: This material is based upon work supported by the National Science Foundation under Grant No. DRL-

  • 1742195. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and

do not necessarily reflect the views of the National Science Foundation.